Math III · N-CN.8

Extend polynomial identities to complex numbers for higher-degree polynomial work.

Extend polynomial identities to complex numbers for higher-degree polynomial work.

Concept Number and Quantity
Domain The Complex Number System
Problem Types

Problem Templates In This Objective

10 problem types are attached to this objective. The full web app handles practice, answers, hints, and walkthroughs.

Template 1

Factor a sum of squares over the complex numbers using conjugate imaginary factors

4 variants
Template 2

Factor an even-power polynomial completely over the complex numbers using conjugate imaginary factors

4 variants
Template 3

Factor a cube polynomial over R and C and list roots

4 variants
Template 4

Multiply complex conjugate linear factors to write a real polynomial

4 variants
Template 5

Verify a complex zero of a real-coefficient polynomial using conjugate factors

4 variants
Template 6

Find all complex roots of an already factored polynomial, including roots from a quadratic that gives a conjugate imaginary pair

4 variants
Template 7

Build the unique monic real polynomial from roots

4 variants
Template 8

Solve a polynomial over the complex numbers by factoring and using conjugate complex factors

4 variants
Template 9

Compare complete factorization over R and C

4 variants
Template 10

List complex roots as repeated multiplicity records

4 variants